Informal division of (10s+40) / s^3+4s^2+3s

Question

for the above informal division why the answer is 2+( (-2s^3-8s^2+4s+40)/(s^3+4s^2+3s))

 

 can anybody explain

 

Answer 1

To see what is going on,  work backwards from the answer.

Long division (or synthetic division)  of

 

(-2s^3-8s^2+4s+40)/(s^3+4s^2+3s)

 

Works out to be -2 with a remainder of (10 s +40) /(s^3 +4 s^2 + 3s)

 

The -2 cancels with the 2  leaving  (10 s +40) /(s^3 +4 s^2 + 3s)

 

I don't know why anyone would look at things this way, but it does work out.